We provide compelling evidence that a previously introduced model of nonperturbative 2D Lorentzian quantum gravity exhibits (two-dimensional) flat-space behavior when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behavior lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different and much ``smoother'' critical behavior.
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Ambjørn et al. (1999) studied this question.
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